Enhancing specific parts of a polyphonic music signal is believed to be a promising way of breaking the glass ceiling that most Music Information Retrieval (MIR) systems are now facing. The use of signal enhancement as a pre-processing step has led to limited improvement though, because distortions inevitably remain in the enhanced signals that may propagate to the subsequent feature extraction and classification stages. Previous studies attempting to reduce the impact of these distortions have relied on the use of feature weighting or missing feature theory. Based on advances in the field of noise-robust speech recognition, we represent the uncertainty about the enhanced signals via a Gaussian distribution instead that is subsequently propagated to the features and to the classifier. We introduce new methods to estimate the uncertainty from the signal in a fully automatic manner and to learn the classifier directly from polyphonic data. We illustrate the results by considering the task of identifying, from a given set of singers, which one is singing at a given time in a given song. Experimental results demonstrate the relevance of our approach.